Is Augmentin 625 safe for children.

My son (12 years old) suffering from cough (moderate intensity) for past few days. Consulted a pediatrician. He prescribed Ascoril D plus cough syrup (7ml 3 times a day) and Levocet 5mg two times a day and did nebuluzation few times. Nebulization helped to reduce cough for few hours, but there wasn't much relief from medicines. Then I met him again and he suggested xray and xray report showed mild lung infection. Not sure if xray was necessary and if it is safe. He prescribed Augmentin 625mg tablet twice a day for 5 days and told to continue medicines and nebulization. I came to know that Augmentin 625 is a very powerful antibiotic and 625mg dose may not be safe for 12 year old child. Probably 375mg would have been better. But I have already given 625mg two times till now (in two days) and I stopped giving syrup. He is feeling better now, but I am worried whether this tablet caused any harm to my son already. Would like to know your opinion. Thanks in advance.